A108505 Number of palindromic semiprimes less than 10^n.

0, 3, 7, 36, 50, 269, 367, 2181, 2816, 18391, 23617, 160773, 203733, 1429749, 1788486, 12808711, 15889727

Offset: 0

Author

Robert G. Wilson v, Jun 06 2005

Keywords

• base
• nonn

Comments

Does the limit n-> inf. a(n+2)/a(n) =~ 8*Pi^2/9?

Crossrefs

Cf. A046328.

Programs

Mathematica

NextPalindrome[n_] := Block[ {l = Floor[ Log[10, n] + 1], idn = IntegerDigits[n]}, If[ Union[ idn] == {9}, Return[n + 2], If[l < 2, Return[n + 1], If[ FromDigits[ Reverse[ Take[ idn, Ceiling[l/2]]]] > FromDigits[ Take[ idn, -Ceiling[l/2]]], FromDigits[ Join[ Take[ idn, Ceiling[l/2]], Reverse[ Take[ idn, Floor[l/2]]] ]], idfhn = FromDigits[ Take[ idn, Ceiling[l/2]]] + 1; idp = FromDigits[ Join[ IntegerDigits[ idfhn], Drop[ Reverse[ IntegerDigits[ idfhn]], Mod[l, 2]]]] ]]]]; fQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; c = np = 0; Do[ While[np < 10^n, If[ fQ[np], c++ ]; np = NextPalindrome[np]]; Print[c], {n, 0, 12}]

Extensions

a(15)-a(16) from Donovan Johnson, Mar 14 2010